Lesson 8
Sort Triangles
Warmup: Estimation Exploration: Angle Measure (10 minutes)
Narrative
This warmup prompts students to estimate the measure of an angle in a triangle. This will be important as they classify triangles in this lesson so will need to distinguish acute, right, and obtuse angles. They will not need to measure angles explicitly but recalling angle measure will help them distinguish the different types of triangles.
Launch
 Groups of 2
 Display the image.
 “What is an estimate that’s too high?” “Too low?” “About right?”
 1 minute: quiet think time
Activity
 “Discuss your thinking with your partner.”
 1 minute: partner discussion
 Record responses.
Student Facing
What is the measure of the angle?
Record an estimate that is:
too low  about right  too high 

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Student Response
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Activity Synthesis
 “How do we know the angle is more than 90 degrees?” (90 degrees is a right angle and this angle is obtuse. It's more than a right angle.)
 “How do we know the angle is less than 180 degrees?” (180 degrees is a straight line and this bends inward so it’s less than 180 degrees.)
Activity 1: The Right Fit (20 minutes)
Narrative
The purpose of this activity is to sort triangles according to their angle measures and side lengths. When they finish sorting, students will notice that two of the possible categories will not have any matching triangles, namely if all 3 sides of a triangle have the same length then the triangle will not have a right angle or an obtuse angle. Students think about whether or not such a triangle could exist and present informal arguments to explain their reasoning (MP3). The activity synthesis formally introduces the category of right triangles.
Supports accessibility for: Language, SocialEmotional Functioning
Required Materials
Materials to Copy
 Card Sort Triangles (Grade 5)
Required Preparation
 Create a set of cards from the blackline master for each group of 2.
Launch
 Groups of 2
 Give each pair of students a set of triangle cards from the blackline master.
Activity
 5 minutes: independent work time
 5 minutes: partner work time
Student Facing
 Find a triangle card that fits in each space on the grid.
 If you don’t think it is possible to find a triangle that fits certain criteria, explain why not.
all three side lengths are different  exactly two of the side lengths are the same  all three side lengths are the same  

has a 90 degree angle  
has an angle that is greater than 90 degrees  
all three angles are less than 90 degrees 
Explanations:
Student Response
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Advancing Student Thinking
If a student needs an entry point into the task, cover the criteria listed in the top row of the table prompt them to find triangles that fit in the criteria listed in the first column. Then, reveal one criteria at a time from the top view and ask, “Which triangle also fits this description?”
Activity Synthesis
 Display a set of triangle cards and a blank table from the workbook. Place the cards in the correct location in the table as you discuss the questions in the synthesis.
 “How did you determine which triangles have 90 degree angles?” (I used the corner of a sheet of paper, measured it using a protractor, or used the grids.)
 “Triangles with a 90 degree angle are called right triangles.”
 “How can we be certain that a triangle is a right triangle?” (We can measure the angles or use the grid.)
 Display shape F.
 “What do you notice about the angles of this triangle?” (One is a 90 degree angle and the other two are equal to each other. The other two are half of a 90 degree angle.)
 “What do you notice about the sides of this triangle?” (Two of them are the same length.)
Activity 2: All, Some, None (15 minutes)
Narrative
The purpose of this activity is for students to sort triangles in a way that makes sense to them and then make observations about right triangles. Students make statements about the right triangle shape cards using the quantifiers all, some, or none. The main shape characteristics students will likely use in their statements are the angle measures, particularly for the two angles that are not right angles, and the side lengths. Students might also choose other characteristics like the orientation of the triangles.
This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.
Required Preparation
 Gather materials from previous activity:
 Triangle Cards
Launch
 Groups of 2 or 4 (if doing a gallery walk)
Activity
 5 minutes: independent work time
 5 minutes: smallgroup work time
MLR7 Compare and Connect
 “Create a visual display that shows your thinking about the problems. You may want to include details such as notes, diagrams, or drawings to help others understand your thinking.”
 2–5 minutes: independent or group work
 5–7 minutes: gallery walk
Student Facing
 Sort the triangle cards from the previous activity in a way that makes sense to you. Describe how you sorted the cards.

Now sort out the triangles with a 90 degree angle. For these triangles, write statements about each category.
 All of the triangles with a 90 degree angle...
 Some of the triangles with a 90 degree angle...
 None of the triangles with a 90 degree angle...
Student Response
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Activity Synthesis
 Invite students to share how they sorted the cards, including
 triangles with a right angle
 triangles with an obtuse angle
 triangles with acute angles
 triangles with no sides equal
 triangles with 2 or more sides equal
 “How did you know which triangle cards have right triangles?” (I used the grid lines. I measured with a protractor. I used the corner of a card.)
 Invite students to share their responses for properties all of the right triangles share.
 Record their responses.
Lesson Synthesis
Lesson Synthesis
“Today we sorted and classified triangles.”
“What are some different ways you can sort triangles?” (We can sort them by angle size and side lengths. We can look for a right angle. We can look for 2 or 3 sides that are the same length.)
“How is classifying triangles the same as classifying quadrilaterals?” (We looked at side lengths and angles in both cases. Right angles were important for both and so were equal side lengths.)
“How is classifying triangles different from classifying quadrilaterals?” (There are fewer sides for triangles and so there are not as many possibilities. A triangle can only have one right angle while a quadrilateral can have as many as 4.)
Cooldown: All, Some, None of the Triangles (5 minutes)
CoolDown
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Student Section Summary
Student Facing
In this section we sorted and analyzed different kinds of quadrilaterals and triangles. We described their properties. For example:
 A rectangle is a quadrilateral with 4 right angles.
 A rhombus is a quadrilateral with 4 equal sides.
 A square is a quadrilateral with 4 right angles and 4 equal sides.
We also described how the shapes are related to each other. For example, we can see that a square is always a rhombus because it has the properties of a rhombus. A square is also always a rectangle because it has the properties of a rectangle. On the other hand, a rectangle does not need to be a square because its side lengths don't have to all be the same. And a rhombus does not need to be a square because its angles do not have to be right angles.